Currently at a price of 1 each 250 popsicles are sold per da

Currently, at a price of $1 each, 250 popsicles are sold per day in the perpetually hot town of Rostin. Consider the elasticity of supply. In the short run, a price increase from $1 to $2 is unit-elastic (E_s = 1). In the long run, a price increase from $1 to $2 has an elasticity of supply of 1.50. (Hint: Apply the midpoints approach to the elasticity of supply.)

a. How many popsicles will be sold each day in the short run if the price rises to $2 each?

     per day.

b. So how many popsicles will be sold per day in the long run if the price rises to $2 each?

     per day.

Solution

We can use the midpoint formula of elasticity to solve the above problem,

Es = [(Q2 - Q1) / {(Q1 + Q2) / 2}] / [(P2 - P1) / {(P1 + P2) / 2 }]

A) In the short run Es = 1 and let Q2 be the quantities sold after change in price from 1 to 2.

1 = [(Q2 - 250) / {(250 + Q2) / 2}] / [(2 - 1) / {(1 + 2) / 2}]

2 / 3 = 2[(Q2 - 250) / (250 + Q2)]

250 + Q2 = 3Q2 - 750

2Q2 = 1000

Q2 = 500

In the short run, 500 units of quantities are sold per day when price increases to 2.

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B) In the long run Es = 1.5 and let Q2 be the quantities sold after change in price from 1 to 2.

1.5 = [(Q2 - 250) / {(250 + Q2) / 2}] / [(2 - 1) / {(1 + 2) / 2}]

1 = (2Q2 - 500) / (250 + Q2)

250 + Q2 = 2Q2 - 500

Q2 = 750

In the long run when price increases to 2 the amount of quantities sold is 750 units per day.